Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints
This paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufact...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-09-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/8/9/279 |
| _version_ | 1818401890604417024 |
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| author | Gao Wang Dachang Zhu Ning Liu Wei Zhao |
| author_facet | Gao Wang Dachang Zhu Ning Liu Wei Zhao |
| author_sort | Gao Wang |
| collection | DOAJ |
| description | This paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufacturing equipment and improve the inherent frequency response of the mechanism. Firstly, a vector-mapping isomorphism between the fully CPM and conventional isomorphic parallel mechanism was constructed with a kinematic differential Jacobian matrix. Then, the mathematical model of topology optimization was put forward considering the compromise programming on the static stiffness and mean vibration-inherent frequency of the mechanism as the design variable and the minimization of compliance as the objective function. A constraint of volume fraction was considered and multi-objective micro displacement mechanism topology optimization based on a prismatic-revolute-revolute (3-PRR) planar nano-positioning continuum structure was performed using the solid isotropic material with penalization (SIMP) technique, which combines the criteria of the optimization algorithm and the vector isomorphic mapping method. Multi-objective topology optimization of the continuum structure micro displacement mechanism was investigated and presented by optimizations with different initial rejection rates. The simulation results show that the stiffness and vibration suppression performance of the continuum structure were improved, whereas the positioning of differential kinematics characteristics of the 3-PRR micro displacement planar fully CPM and isomorphic prototype mechanism retain the same. The modal analysis also provides a rational configuration for the micro displacement mechanism dimensional design and its optimal modal parameters. The crossover oscillation in frequency response of the continuum structure was reduced and quickly converged in the optimization iterations. The performance of the optimized mechanism was verified by the experiments on a planar fully compliant micro displacement continuum structure based on Lead Zirconate Titanate (PZT) actuator. |
| first_indexed | 2024-12-14T07:59:39Z |
| format | Article |
| id | doaj.art-ba5b7f8456e24b17a6dcd0dd2bd32b5b |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-12-14T07:59:39Z |
| publishDate | 2017-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-ba5b7f8456e24b17a6dcd0dd2bd32b5b2022-12-21T23:10:27ZengMDPI AGMicromachines2072-666X2017-09-018927910.3390/mi8090279mi8090279Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and ConstraintsGao Wang0Dachang Zhu1Ning Liu2Wei Zhao3School of Information Science and Technology, Jinan University, Guangzhou 510632, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Information Science and Technology, Jinan University, Guangzhou 510632, ChinaKey Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of China, Jinan University, Guangzhou 510632, ChinaThis paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufacturing equipment and improve the inherent frequency response of the mechanism. Firstly, a vector-mapping isomorphism between the fully CPM and conventional isomorphic parallel mechanism was constructed with a kinematic differential Jacobian matrix. Then, the mathematical model of topology optimization was put forward considering the compromise programming on the static stiffness and mean vibration-inherent frequency of the mechanism as the design variable and the minimization of compliance as the objective function. A constraint of volume fraction was considered and multi-objective micro displacement mechanism topology optimization based on a prismatic-revolute-revolute (3-PRR) planar nano-positioning continuum structure was performed using the solid isotropic material with penalization (SIMP) technique, which combines the criteria of the optimization algorithm and the vector isomorphic mapping method. Multi-objective topology optimization of the continuum structure micro displacement mechanism was investigated and presented by optimizations with different initial rejection rates. The simulation results show that the stiffness and vibration suppression performance of the continuum structure were improved, whereas the positioning of differential kinematics characteristics of the 3-PRR micro displacement planar fully CPM and isomorphic prototype mechanism retain the same. The modal analysis also provides a rational configuration for the micro displacement mechanism dimensional design and its optimal modal parameters. The crossover oscillation in frequency response of the continuum structure was reduced and quickly converged in the optimization iterations. The performance of the optimized mechanism was verified by the experiments on a planar fully compliant micro displacement continuum structure based on Lead Zirconate Titanate (PZT) actuator.https://www.mdpi.com/2072-666X/8/9/279multi-objective topological optimizationdifferential vector isomorphic mapping3-PRR planar micro displacementSIMP |
| spellingShingle | Gao Wang Dachang Zhu Ning Liu Wei Zhao Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints Micromachines multi-objective topological optimization differential vector isomorphic mapping 3-PRR planar micro displacement SIMP |
| title | Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints |
| title_full | Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints |
| title_fullStr | Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints |
| title_full_unstemmed | Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints |
| title_short | Multi-Objective Topology Optimization of a Compliant Parallel Planar Mechanism under Combined Load Cases and Constraints |
| title_sort | multi objective topology optimization of a compliant parallel planar mechanism under combined load cases and constraints |
| topic | multi-objective topological optimization differential vector isomorphic mapping 3-PRR planar micro displacement SIMP |
| url | https://www.mdpi.com/2072-666X/8/9/279 |
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